Risk budgeting and Value-at-Risk

Value-at-Risk (VaR) is a popular risk-metric for reporting financial exposure, for evaluating fund/manager performance and for regulatory disclosures. Yet, VaR is not a coherent risk measure because it is not sub-additive. This paper applies the methodology of risk budgeting to determine if VaR qualifies as a coherent risk measure. We show that the tools of risk budgeting allow VaR to be treated as a coherent risk measure, even though it does not restore sub-additivity. The main finding is that the additional analysis provided by risk budgeting means that VaR is a useful tool even if it is not sub-additive.